International Journal of Optimization in Civil Engineering

OPTIMIZATION PROBLEM IN COMPUTATION OF THE CRITICAL EARTHQUAKE TO EVALUATE THE SUFFICIENCY OF DISCONTINUITY JOINT BASED ON THE IRANIAN STANDARD NO. 2800

R. Kamgar

Earthquakes are random phenomena and there has been no report of similar earthquakes occurring worldwide. Therefore, traditional methods of designing buildings based on past earthquakes with inappropriate discontinuity joints are sometimes ineffective for vital structures. This may lead to collision and destruction of adjacent structures during a severe earthquake. As in the Iranian Standard No. 2800-4, this distance should be at least five-thousandths of the building height from the base level to the adjacent ground boundary for buildings up to eight stories to prevent or reduce this damage. Also, for important or/with more than eight-story buildings, this value is determined using the maximum nonlinear lateral displacement of the structures by considering the effects of the P-delta. Also, if the properties of the adjacent building are not known, this distance should be considered at least equal to 70% of the maximum nonlinear lateral displacement of the structures. The main objective of this study is to investigate the adequacy of the discontinuity joint introduced in the Iranian Standard No. 2800-4 based on the critical excitation method. This method calculates critical earthquakes for three buildings (e.g., three-, seven- and eleven-story moment frames) by considering some constraints on the energy, peak ground acceleration, Fourier amplitude, and strong ground motion duration. The results indicate that the minimum gap between two adjacent buildings derived from the existing codes is lower than those calculated using the critical excitation method. Therefore, oscillation might occur if a structure is designed according to the seismic codes and subjected to a critical earthquake.

GEOMETRIC AND SIZE OPTIMIZATION OF STRUCTURES UNDER NATURAL FREQUENCY CONSTRAINTS USING IMPROVED MATERIAL GENERATION ALGORITHM

V. Goodarzimehr

In this study, the Improved Material Generation Algorithm (IMGA) is proposed to optimize the shape and size of structures. The original Material Generation Algorithm (MGA) introduced an optimization model inspired by the high-level and fundamental characteristics of material chemistry, particularly the configuration of compounds and chemical reactions for generating new materials. MGA uses a Gaussian normal distribution to produce new combinations. To enhance MGA for adapting truss structures, a new technique called Random Chaotic (RC) is proposed. RC increases the speed of convergence and helps escape local optima. To validate the proposed method, several truss structures, including a 37-bar truss bridge, a 52-bar dome, a 72-bar truss, a 120-bar dome, and a 200-bar planar structure, are optimized under natural frequency constraints. Optimizing the shape and size of structures under natural frequency constraints is a significant challenge due to its complexity. Choosing the frequency as a constraint prevents resonance in the structure, which can lead to large deformations and structural failure. Reducing the vibration amplitude of the structure decreases tension and deflection. Consequently, the weight of the structure can be minimized while keeping the frequencies within the permissible range. To demonstrate the superiority of IMGA, its results are compared with those of other state-of-the-art metaheuristic methods. The results show that IMGA significantly improves both exploitation and exploration.

A COHERENCY METRIC TO COMPARE OPTIMALLY CLUSTERED SEISMIC DATA

M. Shahrouzi

Clustering is a well-known solution to deal with complex database features as an unsupervised machine learning technique. One of its practical applications is the selection of non-similar earthquakes for consequent analysis of structural models. In the present work, appropriate clustering of seismic data is searched via optimization. Silhouette value is penalized and used to define the performance objective. A stochastic search algorithm is combined with a greedy search to solve the problem for distinct sets of near–field and far-field ground motion records. The concept of coherency is borrowed from optics to propose a coherency metric for earthquake signals before and after being filtered by structural models. It is then evaluated for various cases of structural response-to-record and response-to-response comparisons. According to the results the proposed coherency detection procedure performs well; confirmed by distinguished structural response spectra between different clusters.

NONLINEAR STRUCTURAL ANALYSIS BY MINIMIZING TWO KINDS OF ENERGIES

M. Rezaiee-Pajand

One of the goals of the nonlinear structural analysis is to reduce the required time for obtaining the numerical solution. More important than this issue, the nonlinear scheme could converge to the answers for all types of problems. A perfect nonlinear solver must have both of these specifications. This article aims to reduce the duration of structural analysis as well as to boost convergent requirements. To reach these two objectives, the authors simultaneously minimize the kinetic and residual structural energies. The ability of the new formulation is shown by solving several structures, with nonlinear geometrical behavior. Based on the compressive studies, numerical solutions show the high efficiency of the new method.

OPTIMIZATION OF SPACE STRUCTURES IN INELASTIC REGION USING FORCE ANALOGY METHOD BASED ON SHUFFLED SHEPHERD OPTIMIZATION ALGORITHM (SSOA)

M.H. Talebpour

The optimization process of space structures considering the nonlinear material behavior requires significant computational efforts due to the large number of design variables and the complexities of nonlinear structural analysis. Accordingly, the Force Analogy Method (FAM) serves as an efficient tool to reduce computational workload and enhance optimization speed. In this study, the weight optimization of space structures in the inelastic region under seismic loading is carried out using the Shuffled Shepherd Optimization Algorithm (SSOA), with the nonlinear structural analysis based on the FAM. To do this, the FAM formulation for axially loaded members of space structures under seismic forces is presented. Subsequently, weight optimization is performed on two double-layer space structures: a flat double-layer structure with 200 members and a barrel vault structure with 729 members under the Kobe earthquake record. Based on the results, the optimized design using the inelastic behavior showed that the FAM provided accurate results when compared to the precise nonlinear structural analysis. The optimized design based on the FAM is considered acceptable, and the computational time for the optimization process has been significantly reduced.

DEVELOPMENT OF EQUIVALENT DAMPING RATIO FOR CONCRETE/STEEL MIXED STRUCTURES CONSIDERING SOIL-STRUCTURE INTERACTION

A. Kaveh

Identification of damping properties for a mixed structure and its interaction with underlying soil is a challenge for structural designers. Current codes and available commercial software packages do not provide analytical solutions for such structural systems. Due to irregular damping ratios, dynamic response of each part of a mixed structure differs significantly. In addition, when the structure is subjected to seismic loads, the soil-structure interaction effects cannot be neglected. To manage these issues, this paper proposes an equivalent damping ratio for mixed structures by means of a semi-empirical error minimization method which considers soil-structure interaction. The results of numerical simulations indicate that the use of the equivalent damping ratios makes the results of dynamics analyses closer to the ones obtained by the actual damping ratios. Consequently, proposed method provides a much better approximation than the case in which the conservative overall ratio of 2% or 5% is used.

A SELF-ADAPTIVE ENHANCED VIBRATING PARTICLE SYSTEM ALGORITHM FOR STRUCTURAL OPTIMIZATION: APPLICATION TO ISCSO BENCHMARK PROBLEMS

P. Hosseini

Structural optimization plays a crucial role in engineering design, aiming to minimize weight and cost while satisfying performance constraints. This research presents a novel Self-Adaptive Enhanced Vibrating Particle System (SA-EVPS) algorithm that automatically adjusts algorithm parameters to improve optimization performance. The algorithm is applied to two challenging examples from the International Student Competition in Structural Optimization (ISCSO) benchmark suite: the 314-member truss structure (ISCSO_2018) and the 345-member truss structure (ISCSO_2021). Results demonstrate that SA-EVPS achieves significantly better solutions compared to previous studies using the Exponential Big Bang-Big Crunch (EBB-BC) algorithm. For ISCSO_2018, SA-EVPS achieved a minimum weight of 16543.57 kg compared to 17934.3 kg for the best EBB-BC variant—a 7.75% improvement. Similarly, for ISCSO_2021, SA-EVPS achieved 4292.71 kg versus 4399.0 kg for the best EBB-BC variant—a 2.42% improvement. The proposed algorithm also demonstrates superior convergence behavior and solution consistency, with coefficients of variation of 3.13% and 1.21% for the two benchmark problems, compared to 12.5% and 2.4% for the best EBB-BC variant. These results highlight the effectiveness of the SA-EVPS algorithm for solving complex structural optimization problems and demonstrate its potential for engineering applications.

NETWORK COMPLEXITY AND STABILITY IN ENVIRONMENTAL SYSTEMS: A GRAPH THEORETIC PERSPECTIVE

R. Sheikholeslami

The stability of large complex systems is a fundamental question in various scientific disciplines, from natural ecosystems to engineered environmental networks. This paper examines the interplay between network complexity and stability through the lens of graph theory and spectral analysis, based on Robert May’s seminal work on stability in randomly connected networks. Environmental systems are modeled as graphs in which components, such as reservoirs in a water distribution system or physical processes in hydrological cycle, interact through defined connections of varying strengths. Stability in these networks depends on the level of connectivity, the number of interacting components, and the strength of interactions between them. Previous studies have shown that as a system becomes more interconnected, it reaches a threshold beyond which it transitions sharply from stability to instability. Using concepts from spectral graph theory, we show how structural properties of an environmental network—such as degree distribution, modularity, and spectral characteristics—shape stability. Two numerical examples are presented to illustrate how increasing connectivity affects stability in water resource networks modeled as random graphs. The results suggest that systems with many weak interactions are generally more stable, whereas systems with fewer but stronger interactions are more prone to instability unless their structure is carefully managed. These insights provide valuable insights for designing resilient environmental networks and optimizing the management of interconnected natural and engineered systems.